Open Access

Epsilon Nielsen fixed point theory

Fixed Point Theory and Applications20062006:29470

DOI: 10.1155/FPTA/2006/29470

Received: 11 October 2004

Accepted: 21 July 2005

Published: 18 March 2006

Abstract

Let be a map of a compact, connected Riemannian manifold, with or without boundary. For sufficiently small, we introduce an -Nielsen number that is a lower bound for the number of fixed points of all self-maps of that are -homotopic to . We prove that there is always a map that is -homotopic to such that has exactly fixed points. We describe procedures for calculating for maps of -manifolds.

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Authors’ Affiliations

(1)
Department of Mathematics, University of California

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Copyright

© Robert F. Brown. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.